Question: What's the first wrong statement in the proof below that $ \triangle EBC \cong \triangle ABC$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle BAC \cong \angle BED$ $, \ $ $ \overline{AC} \cong \overline{DE}$ $, \ $ $ \angle ACB \cong \angle BDE$ $, \ $ $ \overline{BC} \cong \overline{CF}$ $, \ $ $ \angle ABC \cong \angle CFE$ $, \ $ and $\ $ $ \angle BAC \cong \angle CEF$ Proof $ \triangle EBD \cong \triangle ABC$ because ASA $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \angle BDE \cong \angle CBE$ because corresponding parts of congruent triangles are congruent $ \angle DBE \cong \angle ABC$ because corresponding parts of congruent triangles are congruent $ \triangle ABC \cong \triangle EFC$ because AAS $ \triangle EBC \cong \triangle ABC$ because SSS
Explanation: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle CBE \cong \angle BDE$ is the first wrong statement.